Quantum phase entropy and entanglement of a multiphoton three-level atom near the edge of a photonic band gap

Abstract

Motivated by recent developments in quantum entanglement, we study the relations among concurrence and phase entropy of a three-level atom interacting with a bimodal cavity field. Analytical results are presented when the photonic band gap is exhibited by the presence of photonic crystals. The evolution of the atomic inversion with the field initially in a coherent state is examined, and different nonclassical effects in its dynamics are discussed. An extension of the notion of concurrence introduced by Wooters is used to quantify the entanglement. We conclusively calculate the phase entropy and entanglement using the Pegg-Barnett phase formalism. Evidence has been found to support the idea that phase entropy and concurrence are correlated in this particular model. One feature of the regime considered here is that closed-form evaluation of the time evolution may be carried out in the presence of the detuning and the photonic band gap, which provides insight into the difference in the nature of the concurrence function for atom-field coupling, mode frequency, and different cavity parameters. We demonstrate how fluctuations in the concurrence and phase entropy are affected by the presence of the photonic band gap. Explicit results with numerical simulations applied to GaAs are obtained.